5 papers · 1 filter
Composition algebras in symmetric tensor categories
Alberto Elduque, Javier Rández-Ibáñez
Composition algebras in symmetric tensor categories are defined. The classical results on standard unital composition algebras, as well as the classification of the unital composit…
Solvable Quadratic Lie algebras up to dimension 7
Pilar Benito, Javier Rández-Ibáñez
The double extension method allows the construction of quadratic Lie algebras from smaller ones. Using this approach, in this work we describe all solvable indecomposable quadratic…
Vidinli algebras
Alberto Elduque, Javier Rández-Ibáñez
A new class of nonassociative algebras, Vidinli algebras, is defined based on recent work of Coşkun and Eden. These algebras are conic (or quadratic) algebras with the extra restri…
Computing Derivations on Nilpotent Quadratic Lie Algebras
Pilar Benito, Javier Rández-Ibáñez, Jorge Roldán-López
Every non-solvable and non-semisimple quadratic Lie algebra can be obtained as a double extension of a solvable quadratic Lie algebra. Thanks to a partial classification of nilpote…
Skew-adjoint maps and quadratic Lie algebras
Pilar Benito, Javier Rández-Ibáñez, Jorge Roldán-López
The procedure of double extension of vector spaces endowed with non-degenerate bilinear forms allows us to introduce the class of generalized $\mbK$-oscillator algebras over any ar…